params
## $n_sims
## [1] 1000
## 
## $n_sites
## [1] 200
library(flocker)
library(brms)
## Loading required package: Rcpp
## Loading 'brms' package (version 2.20.0). Useful instructions
## can be found by typing help('brms'). A more detailed introduction
## to the package is available through vignette('brms_overview').
## 
## Attaching package: 'brms'
## The following object is masked from 'package:stats':
## 
##     ar
library(SBC)
set.seed(3)

Overview

This document performs simulation-based calibration for the models available in R package flocker. Here, our goal is to validate flocker’s data formatting, decoding, and likelihood implementations, and not brms’s construction of the linear predictors.

The encoding of the data for a flocker model tends to be more complex in the presence of missing observations, and so we include missingness in the data simulation wherever possible (some visits missing in all models, some time-steps missing in multiseason models).

In all models, we include one unit covariate that affects detection and occupancy, colonization, extinction and/or autologistic terms as applicable, and one event covariate that affects detection only (for all models except the rep-constant).

Single-season

Rep-constant

# make the stancode
model_name <- paste0(tempdir(), "/sbc_rep_constant_model.stan")
fd <- simulate_flocker_data(
  n_pt = params$n_sites, n_sp = 1,
  params = list(
    coefs = data.frame(
      det_intercept = rnorm(1),
      det_slope_unit = rnorm(1),
      occ_intercept = rnorm(1),
      occ_slope_unit = rnorm(1)
    )
  ),
  seed = NULL,
  rep_constant = TRUE,
  ragged_rep = TRUE
)
flocker_data = make_flocker_data(fd$obs, fd$unit_covs, quiet = TRUE)
  
scode <- flocker_stancode(
    f_occ = ~ 0 + Intercept + uc1,
    f_det = ~ 0 + Intercept + uc1,
    flocker_data = flocker_data,
    prior = 
      brms::set_prior("std_normal()") + 
      brms::set_prior("std_normal()", dpar = "occ"),
    backend = "cmdstanr"
  )

writeLines(scode, model_name)

rep_constant_generator <- function(N){  
  fd <- simulate_flocker_data(
    n_pt = N, n_sp = 1,
    params = list(
      coefs = data.frame(
        det_intercept = rnorm(1),
        det_slope_unit = rnorm(1),
        occ_intercept = rnorm(1),
        occ_slope_unit = rnorm(1)
      )
    ),
    seed = NULL,
    rep_constant = TRUE,
    ragged_rep = TRUE
  )
  
  flocker_data = make_flocker_data(fd$obs, fd$unit_covs, quiet = TRUE)
  
  # format for return
  list(
    variables = list(
      `b[1]` = fd$params$coefs$det_intercept,
      `b[2]` = fd$params$coefs$det_slope_unit,
      `b_occ[1]` = fd$params$coefs$occ_intercept,
      `b_occ[2]` = fd$params$coefs$occ_slope_unit
    ),
    generated = flocker_standata(
      f_occ = ~ 0 + Intercept + uc1,
      f_det = ~ 0 + Intercept + uc1,
      flocker_data = flocker_data
    )
  )
}

rep_constant_gen <- SBC_generator_function(
  rep_constant_generator, 
  N = params$n_sites
  )
rep_constant_dataset <- suppressMessages(
  generate_datasets(rep_constant_gen, params$n_sims)
)
  
rep_constant_backend <- 
  SBC_backend_cmdstan_sample(
    cmdstanr::cmdstan_model(
      paste0(tempdir(), "/sbc_rep_constant_model.stan")
      )
    )

rep_constant_results <- compute_SBC(rep_constant_dataset, rep_constant_backend)

plot_ecdf(rep_constant_results)

plot_rank_hist(rep_constant_results)

plot_ecdf_diff(rep_constant_results)

Rep-varying

# make the stancode
model_name <- paste0(tempdir(), "/sbc_rep_varying_model.stan")
fd <- simulate_flocker_data(
  n_pt = params$n_sites, n_sp = 1,
  params = list(
    coefs = data.frame(
      det_intercept = rnorm(1),
      det_slope_unit = rnorm(1),
      det_slope_visit = rnorm(1),
      occ_intercept = rnorm(1),
      occ_slope_unit = rnorm(1)
    )
  ),
  seed = NULL,
  rep_constant = FALSE,
  ragged_rep = TRUE
)
flocker_data = make_flocker_data(fd$obs, fd$unit_covs, fd$event_covs, quiet = TRUE)
  
scode <- flocker_stancode(
    f_occ = ~ 0 + Intercept + uc1,
    f_det = ~ 0 + Intercept + uc1 + ec1,
    flocker_data = flocker_data,
    prior = 
      brms::set_prior("std_normal()") + 
      brms::set_prior("std_normal()", dpar = "occ"),
    backend = "cmdstanr"
  )
writeLines(scode, model_name)

rep_varying_generator <- function(N){  
  fd <- simulate_flocker_data(
    n_pt = N, n_sp = 1,
    params = list(
      coefs = data.frame(
        det_intercept = rnorm(1),
        det_slope_unit = rnorm(1),
        det_slope_visit = rnorm(1),
        occ_intercept = rnorm(1),
        occ_slope_unit = rnorm(1)
      )
    ),
    seed = NULL,
    rep_constant = FALSE,
    ragged_rep = TRUE
  )
  
  flocker_data = make_flocker_data(fd$obs, fd$unit_covs, fd$event_covs, quiet = TRUE)
  
  # format for return
  list(
    variables = list(
      `b[1]` = fd$params$coefs$det_intercept,
      `b[2]` = fd$params$coefs$det_slope_unit,
      `b[3]` = fd$params$coefs$det_slope_visit,
      `b_occ[1]` = fd$params$coefs$occ_intercept,
      `b_occ[2]` = fd$params$coefs$occ_slope_unit
    ),
    generated = flocker_standata(
      f_occ = ~ 0 + Intercept + uc1,
      f_det = ~ 0 + Intercept + uc1 + ec1,
      flocker_data = flocker_data
    )
  )
}

rep_varying_gen <- SBC_generator_function(
  rep_varying_generator, 
  N = params$n_sites
  )
rep_varying_dataset <- suppressMessages(
  generate_datasets(rep_varying_gen, params$n_sims)
)
  
rep_varying_backend <- 
  SBC_backend_cmdstan_sample(
    cmdstanr::cmdstan_model(
      paste0(tempdir(), "/sbc_rep_varying_model.stan")
      )
    )

rep_varying_results <- compute_SBC(rep_varying_dataset, rep_varying_backend)

plot_ecdf(rep_varying_results)

plot_rank_hist(rep_varying_results)

plot_ecdf_diff(rep_varying_results)

Multi-season

flocker fits multi-season models that parameterize the dynamics using colonization/extinction or autologistic specifications, and that parameterize the initial occupancy state using explicit and equilibrium parameterizations, for a total of four classes of multi-season model. We validate each class.

Colonization-extinction, explicit initial occupancy

# make the stancode
model_name <- paste0(tempdir(), "/sbc_colex_ex_model.stan")
fd <- simulate_flocker_data(
  n_pt = params$n_sites, n_sp = 1, n_season = 4,
  params = list(
    coefs = data.frame(
      det_intercept = rnorm(1),
      det_slope_unit = rnorm(1),
      det_slope_visit = rnorm(1),
      occ_intercept = rnorm(1),
      occ_slope_unit = rnorm(1),
      col_intercept = rnorm(1),
      col_slope_unit = rnorm(1),
      ex_intercept = rnorm(1),
      ex_slope_unit = rnorm(1)
    )
  ),
  seed = NULL,
  rep_constant = FALSE,
  multiseason = "colex",
  multi_init = "explicit",
  ragged_rep = TRUE
)
flocker_data = make_flocker_data(
  fd$obs, fd$unit_covs, fd$event_covs,
  type = "multi", quiet = TRUE)
  
scode <- flocker_stancode(
    f_occ = ~ 0 + Intercept + uc1,
    f_col = ~ 0 + Intercept + uc1,
    f_ex = ~ 0 + Intercept + uc1,
    f_det = ~ 0 + Intercept + uc1 + ec1,
    flocker_data = flocker_data,
    prior = 
      brms::set_prior("std_normal()") + 
      brms::set_prior("std_normal()", dpar = "occ") +
      brms::set_prior("std_normal()", dpar = "colo") +
      brms::set_prior("std_normal()", dpar = "ex"),
    multiseason = "colex",
    multi_init = "explicit",
    backend = "cmdstanr"
  )
writeLines(scode, model_name)

colex_ex_generator <- function(N){  
  fd <- simulate_flocker_data(
    n_pt = params$n_sites, n_sp = 1, n_season = 4,
    params = list(
        det_intercept = rnorm(1),
        det_slope_unit = rnorm(1),
        det_slope_visit = rnorm(1),
        occ_intercept = rnorm(1),
        occ_slope_unit = rnorm(1),
        colo_intercept = rnorm(1),
        colo_slope_unit = rnorm(1),
        ex_intercept = rnorm(1),
        ex_slope_unit = rnorm(1)
    ),
    seed = NULL,
    rep_constant = FALSE,
    multiseason = "colex",
    multi_init = "explicit",
    ragged_rep = TRUE
  )
  
  flocker_data = make_flocker_data(
    fd$obs, fd$unit_covs, fd$event_covs,
    type = "multi", quiet = TRUE)
  
  # format for return
  list(
    variables = list(
      `b[1]` = fd$params$coefs$det_intercept,
      `b[2]` = fd$params$coefs$det_slope_unit,
      `b[3]` = fd$params$coefs$det_slope_visit,
      `b_occ[1]` = fd$params$coefs$occ_intercept,
      `b_occ[2]` = fd$params$coefs$occ_slope_unit,
      `b_colo[1]` = fd$params$coefs$col_intercept,
      `b_colo[2]` = fd$params$coefs$col_slope_unit,
      `b_ex[1]` = fd$params$coefs$ex_intercept,
      `b_ex[2]` = fd$params$coefs$ex_slope_unit
    ),
    generated = flocker_standata(
      f_occ = ~ 0 + Intercept + uc1,
      f_col = ~ 0 + Intercept + uc1,
      f_ex = ~ 0 + Intercept + uc1,
      f_det = ~ 0 + Intercept + uc1 + ec1,
      flocker_data = flocker_data,
      multiseason = "colex",
      multi_init = "explicit"
    )
  )
}

colex_ex_gen <- SBC_generator_function(
  colex_ex_generator, 
  N = params$n_sites
  )
colex_ex_dataset <- suppressMessages(
  generate_datasets(colex_ex_gen, params$n_sims)
)
  
colex_ex_backend <- 
  SBC_backend_cmdstan_sample(
    cmdstanr::cmdstan_model(
      paste0(tempdir(), "/sbc_colex_ex_model.stan")
      )
    )

colex_ex_results <- compute_SBC(colex_ex_dataset, colex_ex_backend)

plot_ecdf(colex_ex_results)

plot_rank_hist(colex_ex_results)

plot_ecdf_diff(colex_ex_results)

Colonization-extinction, equilibrium initial occupancy

# make the stancode
model_name <- paste0(tempdir(), "/sbc_colex_eq_model.stan")
fd <- simulate_flocker_data(
  n_pt = params$n_sites, n_sp = 1, n_season = 4,
  params = list(
      det_intercept = rnorm(1),
      det_slope_unit = rnorm(1),
      det_slope_visit = rnorm(1),
      colo_intercept = rnorm(1),
      colo_slope_unit = rnorm(1),
      ex_intercept = rnorm(1),
      ex_slope_unit = rnorm(1)
  ),
  seed = NULL,
  rep_constant = FALSE,
  multiseason = "colex",
  multi_init = "equilibrium",
  ragged_rep = TRUE
)
flocker_data = make_flocker_data(
  fd$obs, fd$unit_covs, fd$event_covs,
  type = "multi", quiet = TRUE)
  
scode <- flocker_stancode(
  f_col = ~ 0 + Intercept + uc1,
  f_ex = ~ 0 + Intercept + uc1,
  f_det = ~ 0 + Intercept + uc1 + ec1,
  flocker_data = flocker_data,
  prior = 
    brms::set_prior("std_normal()") + 
    brms::set_prior("std_normal()", dpar = "colo") +
    brms::set_prior("std_normal()", dpar = "ex"),
  multiseason = "colex",
  multi_init = "equilibrium",
  backend = "cmdstanr"
  )
writeLines(scode, model_name)

colex_eq_generator <- function(N){  
  fd <- simulate_flocker_data(
    n_pt = params$n_sites, n_sp = 1, n_season = 4,
    params = list(
        det_intercept = rnorm(1),
        det_slope_unit = rnorm(1),
        det_slope_visit = rnorm(1),
        col_intercept = rnorm(1),
        col_slope_unit = rnorm(1),
        ex_intercept = rnorm(1),
        ex_slope_unit = rnorm(1)
    ),
    seed = NULL,
    rep_constant = FALSE,
    multiseason = "colex",
    multi_init = "equilibrium",
    ragged_rep = TRUE
  )
  
  flocker_data = make_flocker_data(
    fd$obs, fd$unit_covs, fd$event_covs,
    type = "multi", quiet = TRUE)
  
  # format for return
  list(
    variables = list(
      `b[1]` = fd$params$coefs$det_intercept,
      `b[2]` = fd$params$coefs$det_slope_unit,
      `b[3]` = fd$params$coefs$det_slope_visit,
      `b_colo[1]` = fd$params$coefs$col_intercept,
      `b_colo[2]` = fd$params$coefs$col_slope_unit,
      `b_ex[1]` = fd$params$coefs$ex_intercept,
      `b_ex[2]` = fd$params$coefs$ex_slope_unit
    ),
    generated = flocker_standata(
      f_col = ~ 0 + Intercept + uc1,
      f_ex = ~ 0 + Intercept + uc1,
      f_det = ~ 0 + Intercept + uc1 + ec1,
      flocker_data = flocker_data,
      multiseason = "colex",
      multi_init = "equilibrium"
    )
  )
}

colex_eq_gen <- SBC_generator_function(
  colex_eq_generator, 
  N = params$n_sites
  )
colex_eq_dataset <- suppressMessages(
  generate_datasets(colex_eq_gen, params$n_sims)
)
  
colex_eq_backend <- 
  SBC_backend_cmdstan_sample(
    cmdstanr::cmdstan_model(
      paste0(tempdir(), "/sbc_colex_eq_model.stan")
      )
    )

colex_eq_results <- compute_SBC(colex_eq_dataset, colex_eq_backend)
##  - 865 (86%) fits had some steps rejected. Maximum number of rejections was 4.
## Not all diagnostics are OK.
## You can learn more by inspecting $default_diagnostics, $backend_diagnostics 
## and/or investigating $outputs/$messages/$warnings for detailed output from the backend.
plot_ecdf(colex_eq_results)

plot_rank_hist(colex_eq_results)

plot_ecdf_diff(colex_eq_results)

Autologistic, explicit initial occupancy

# make the stancode
model_name <- paste0(tempdir(), "/sbc_auto_ex_model.stan")
fd <- simulate_flocker_data(
  n_pt = params$n_sites, n_sp = 1, n_season = 4,
  params = list(
      det_intercept = rnorm(1),
      det_slope_unit = rnorm(1),
      det_slope_visit = rnorm(1),
      occ_intercept = rnorm(1),
      occ_slope_unit = rnorm(1),
      col_intercept = rnorm(1),
      col_slope_unit = rnorm(1),
      auto_intercept = rnorm(1),
      auto_slope_unit = rnorm(1)
  ),
  seed = NULL,
  rep_constant = FALSE,
  multiseason = "autologistic",
  multi_init = "explicit",
  ragged_rep = TRUE
)
flocker_data = make_flocker_data(
  fd$obs, fd$unit_covs, fd$event_covs,
  type = "multi", quiet = TRUE)
  
scode <- flocker_stancode(
    f_occ = ~ 0 + Intercept + uc1,
    f_col = ~ 0 + Intercept + uc1,
    f_auto = ~ 0 + Intercept + uc1,
    f_det = ~ 0 + Intercept + uc1 + ec1,
    flocker_data = flocker_data,
    prior = 
      brms::set_prior("std_normal()") + 
      brms::set_prior("std_normal()", dpar = "occ") +
      brms::set_prior("std_normal()", dpar = "colo") +
      brms::set_prior("std_normal()", dpar = "autologistic"),
    multiseason = "autologistic",
    multi_init = "explicit",
    backend = "cmdstanr"
  )
writeLines(scode, model_name)

auto_ex_generator <- function(N){  
  fd <- simulate_flocker_data(
    n_pt = params$n_sites, n_sp = 1, n_season = 4,
    params = list(
        det_intercept = rnorm(1),
        det_slope_unit = rnorm(1),
        det_slope_visit = rnorm(1),
        occ_intercept = rnorm(1),
        occ_slope_unit = rnorm(1),
        colo_intercept = rnorm(1),
        colo_slope_unit = rnorm(1),
        auto_intercept = rnorm(1),
        auto_slope_unit = rnorm(1)
    ),
    seed = NULL,
    rep_constant = FALSE,
    multiseason = "autologistic",
    multi_init = "explicit",
    ragged_rep = TRUE
  )
  
  flocker_data = make_flocker_data(
    fd$obs, fd$unit_covs, fd$event_covs,
    type = "multi", quiet = TRUE)
  
  # format for return
  list(
    variables = list(
      `b[1]` = fd$params$coefs$det_intercept,
      `b[2]` = fd$params$coefs$det_slope_unit,
      `b[3]` = fd$params$coefs$det_slope_visit,
      `b_occ[1]` = fd$params$coefs$occ_intercept,
      `b_occ[2]` = fd$params$coefs$occ_slope_unit,
      `b_colo[1]` = fd$params$coefs$col_intercept,
      `b_colo[2]` = fd$params$coefs$col_slope_unit,
      `b_autologistic[1]` = fd$params$coefs$auto_intercept,
      `b_autologistic[2]` = fd$params$coefs$auto_slope_unit
    ),
    generated = flocker_standata(
      f_occ = ~ 0 + Intercept + uc1,
      f_col = ~ 0 + Intercept + uc1,
      f_auto = ~ 0 + Intercept + uc1,
      f_det = ~ 0 + Intercept + uc1 + ec1,
      flocker_data = flocker_data,
      multiseason = "autologistic",
      multi_init = "explicit"
    )
  )
}

auto_ex_gen <- SBC_generator_function(
  auto_ex_generator, 
  N = params$n_sites
  )
auto_ex_dataset <- suppressMessages(
  generate_datasets(auto_ex_gen, params$n_sims)
)
  
auto_ex_backend <- 
  SBC_backend_cmdstan_sample(
    cmdstanr::cmdstan_model(
      paste0(tempdir(), "/sbc_auto_ex_model.stan")
      )
    )

auto_ex_results <- compute_SBC(auto_ex_dataset, auto_ex_backend)

plot_ecdf(auto_ex_results)

plot_rank_hist(auto_ex_results)

plot_ecdf_diff(auto_ex_results)

Autologistic, equilibrium initial occupancy

# make the stancode
model_name <- paste0(tempdir(), "/sbc_auto_eq_model.stan")
fd <- simulate_flocker_data(
  n_pt = params$n_sites, n_sp = 1, n_season = 4,
  params = list(
      det_intercept = rnorm(1),
      det_slope_unit = rnorm(1),
      det_slope_visit = rnorm(1),
      auto_intercept = rnorm(1),
      auto_slope_unit = rnorm(1)
  ),
  seed = NULL,
  rep_constant = FALSE,
  multiseason = "autologistic",
  multi_init = "equilibrium",
  ragged_rep = TRUE
)
flocker_data = make_flocker_data(
  fd$obs, fd$unit_covs, fd$event_covs,
  type = "multi", quiet = TRUE)
  
scode <- flocker_stancode(
    f_col = ~ 0 + Intercept + uc1,
    f_auto = ~ 0 + Intercept + uc1,
    f_det = ~ 0 + Intercept + uc1 + ec1,
    flocker_data = flocker_data,
    prior = 
      brms::set_prior("std_normal()") + 
      brms::set_prior("std_normal()", dpar = "colo") +
      brms::set_prior("std_normal()", dpar = "autologistic"),
    multiseason = "autologistic",
    multi_init = "equilibrium",
    backend = "cmdstanr"
  )
writeLines(scode, model_name)

auto_eq_generator <- function(N){  
  fd <- simulate_flocker_data(
    n_pt = params$n_sites, n_sp = 1, n_season = 4,
    params = list(
        det_intercept = rnorm(1),
        det_slope_unit = rnorm(1),
        det_slope_visit = rnorm(1),
        col_intercept = rnorm(1),
        col_slope_unit = rnorm(1),
        auto_intercept = rnorm(1),
        auto_slope_unit = rnorm(1)
    ),
    seed = NULL,
    rep_constant = FALSE,
    multiseason = "autologistic",
    multi_init = "equilibrium",
    ragged_rep = TRUE
  )
  
  flocker_data = make_flocker_data(
    fd$obs, fd$unit_covs, fd$event_covs,
    type = "multi", quiet = TRUE)
  
  # format for return
  list(
    variables = list(
      `b[1]` = fd$params$coefs$det_intercept,
      `b[2]` = fd$params$coefs$det_slope_unit,
      `b[3]` = fd$params$coefs$det_slope_visit,
      `b_colo[1]` = fd$params$coefs$col_intercept,
      `b_colo[2]` = fd$params$coefs$col_slope_unit,
      `b_autologistic[1]` = fd$params$coefs$auto_intercept,
      `b_autologistic[2]` = fd$params$coefs$auto_slope_unit
    ),
    generated = flocker_standata(
      f_col = ~ 0 + Intercept + uc1,
      f_auto = ~ 0 + Intercept + uc1,
      f_det = ~ 0 + Intercept + uc1 + ec1,
      flocker_data = flocker_data,
      multiseason = "autologistic",
      multi_init = "equilibrium"
    )
  )
}

auto_eq_gen <- SBC_generator_function(
  auto_eq_generator, 
  N = params$n_sites
  )
auto_eq_dataset <- suppressMessages(
  generate_datasets(auto_eq_gen, params$n_sims)
)
  
auto_eq_backend <- 
  SBC_backend_cmdstan_sample(
    cmdstanr::cmdstan_model(
      paste0(tempdir(), "/sbc_auto_eq_model.stan")
      )
    )

auto_eq_results <- compute_SBC(auto_eq_dataset, auto_eq_backend)
##  - 319 (32%) fits had some steps rejected. Maximum number of rejections was 4.
## Not all diagnostics are OK.
## You can learn more by inspecting $default_diagnostics, $backend_diagnostics 
## and/or investigating $outputs/$messages/$warnings for detailed output from the backend.
plot_ecdf(auto_eq_results)

plot_rank_hist(auto_eq_results)

plot_ecdf_diff(auto_eq_results)